The aim of this paper is to point out inappropriate definitions of addition and multiplication operations over Atanassov’s intuitionistic fuzzy sets (IFS) and incorrect formal equivalence between the Atanassov’s IFS and the interval-valued fuzzy set. We strongly suggest that algebraic operations over Atanassov’s IFSs are redefined by using the extension principle, which is not yet established for Atanassov’s IFSs.
